Of all materials magnesia is one of the few minerals the properties of which dramatically alter depending on the source, temperature of calcination or whether other components are present during calcination. Quite distinct and separate properties ensue and different markets exist for the different forms of magnesia that result.

There are many grades of mangesia. TecEco have introduced a new grade we have called Reactive magnesia for use in cements which we have defined as magnesia calcined at less than about 750°C and ground to a particle size with greater than 95% of the particles of less than 120 microns and for most implementations of our cement technology less than 45 microns. In practice we engineer the temperature of calcination and particle size with the application in mind and form many formulations we point out that magnesia calcined as 650 °C passing 45 micron or less is better.. For Tec-Cement concretes the mean particle size is around 5 - 7 micron and designed to fit in between Portland cement Particles so as to reduce not increase water demand. A slightly coarser grind is generally used for Eco-Cement concretes so the particles do not fit between cement grains

This page discusses all aspects of magensia including markets, acceptance of the term "reactive magnesia" by scientists as well as the influence of ore type, impurities and temperature of calcination on properties

Separate Markets for Different Grades

Different grades of magnesia other than the reactive magnesia grade we have introduced already exist and have different properties and define different markets.

Industrial Minerals is the leading communicator in the world of magnesium compounds and their magnesia page on their web site makes it clear that different sources and processing conditions including the temperature of calcination define different products used in different markets.

According to Dr Mark Shand, the author of the only authoratative text book on magnesia, " magnesium oxide........has a number of categories, namely, light - burned or caustic -calcined MgO, hard burn MgO, and dead burn MgO, or as it is otherwise known, periclase; and the last category, fused magnesia.

Light-burn of caustic-calcined MgO refers to a product that has been calcined at the lower end of the temperatue spectrum, typically 1500-1700 deg F (815 - 926 deg C). This product typically has the highest reactivity and greatest specific surface area of the entire magnesium oxide catefory. Hard-burn MgO is calcined at a higher temperature, 2400-2800 deg F (1316 - 1537 deg C), and has a correspondingly lower reactivity and surface area. Dead burn MgO, or periclase, is produced at temperatures above 2800 deg F (1537 deg C), which having a very small surface aera, makes it unreactive. Finally, fused magnesia, produced at temperatures above the fusion point of magnesium oxide ( 2800 deg C) (5072 def F) is the least reactive." [2]

“magnesite from different types of deposits and of different degrees of purity has different uses. The purchaser of refractory brick requires a low lime grade and prefers the material carrying some iron because he has found it most suitable. The purchaser of crude magnesite for the manufacture of CO2 is not so rigorous in his requirements [3]"

Sources of Raw Materials

The source of magnesite or other mineral used to make magnesia has a significant effect on the properties of the material produced. This is for two reasons, impurities vary and hence properties. There is also a tendency during calcination to pseudomorph the orginal microstructure whereby properties are also affected. “Geological occurrences of magnesite are either microcrystalling (micritic) or macrocrystalline (sparry). There are three geological modes of magnesite occurrence: 1) Small scale micritic deposits…2) Laterally continuous, stratiform sediment hosted depsits, which can be cryptocrystalline (micritic) or coarsely crystalline (sparry)…3) Clustered hydrothermal deposits that form sparry magnesites at or near ultramafic complexes [4]”

Impurities

Magnesia can not be produced effectively or efficientily by co-calcination with other minerals.
Magnesia can be made from a mixture of magnesite and limestone or for that matter from dolomite, however in both cases fluxes are generally required, there are separation difficulties and there is no market for magnesia mixed with other minerals. As a consequence we do not know of any profitable commercial processes that use a mixed magnesium calcium kilon input. For the production of cement grade reactive magnesia sources with low quantities of impurities other than silica or calcium should be used because if magnesite or some other source material is calcined with minerals such as iron at an elevated temperature, other reactions tend to occur that will alter the magnesia by forming something else in association with it.

The Affect of Temperature of Calcination

Theoretical considerations

Acceptance by Scientists that Lower Temperatures Produce more Reactive Product

The characterisation of different magnesium oxide products according to calcination temperature is recognised by the International Cement and Concrete Scientific Community.

Mark Shand quoted above wrote his text book in 2006 and was not aware of a fifth grade of magnesia we have introduced into the literature called reactive magnesia as defined above. This term is now used by all universities working on reactive magnesium cements including Cambridge university, Imperial College London, and The University of Technology, Sydney. It has found its way into dictionaries and is clearly a much more reactive magnesia than loosely encompassed or even contemplated by the caustic calcined grade. At Magmin 2010 [5] John Harrison suggested that a new category for Reactive Magnesia should be created and used and the proposition was generally accepted but not officially.

Researchers at Cambridge University recently had this to say "One area for research into partial cement replacements is the recently emerged family of reactive magnesia (MgO) cements. These cement formulations developed and patented a few years ago by the Australian scientist John Harrison, are blends of PC and reactive MgO in different proportions depending on the intended application, ranging from structural concrete to porous masonry units. They have been developed with strong emphasis on a range of sustainability advantages over PC and have received significant publicity including coverage in New Scientist and the Guardian.

The potential for significant CO2 sequestration within porous masonry units containing reactive MgO as the cement component and the associated significant increase in strength are the subject of this paper" [6]

Why Low Temperature Calcined MgO is more Reactive

At a temperature range between (250 °C - 800 °C ++ ), MgCO3 decomposes to magnesium oxide and carbon dioxide with a reaction enthalpy 118.28 kJ / mole as shown in the diagram to the left. The process is called calcining:

MgCO3 -{250-800 °C}=> MgO + CO2

Above about 500 °C the process will reach reach completion with 100% conversion to MgO.

The lattice energy of a crystalline solid is
the energy required to separate completely a mole of a solid ionic compound into its gaseous ions. It is based on a mole and applies to atoms in a lattice and is a measure of just how much stabilization results from the arranging of oppositely charged ions in an ionic solid. The more each atom of magnesium and oxygen are surrounded by other atoms of magnesium and oxygen in an orderly way, the more crystalline and ordered the structure and the higher the lattice energy. High temperature calcination results in a much more ordered crystalline product than low temperature calcination. With lower temperature calcination, not only are there more surfaces, they are more disordered with a higher number of coordinate unsaturated sites.

Although we have in the past defines reactivity with reference to lattice energy we could have just as correctly defined it in relation to the proportion of coordinate unsaturated sites compared to saturated sites. As both are not possible to directly measure scientists with an interest in MgO talk about specific surface area (SSA or Blaine) being the relevant factor for reactivity. SSA or Blaine, coordinate saturation and lattice energy are all related. The higher the specific surface area the more surfaces there are such as on corners or fissures and other imperfections and the more atoms that are close to the surface that are not coordinately saturated and therefore easily detached by strongly polar water molecules. Proton wrenching is thought to be the mechanism of dissolution by Stumm and Marini [7][8], however according to Fruwirth et. al. there are other mechanisms at higher pH [9].

If the temperature of calcination is high then as might be expected some of the excess energy over what is required for the decomposition reaction shown in the diagram goes into creating larger more ordered crystallites and is thus converted to lattice energy. Energy is used to reduce the entropy of the crystal however more entropy is lost to the system through heat wasted. (See discussion on entropy below)

Bonding coulomb forces are less at the surface, on corners etc and a few substantially ionically bound atoms of magnesium and oxygen have less lattice energy (because there are more surfaces, corners etc.) than a large number of ionically bound atoms of magnesium and oxygen. It takes energy to put them together and energy to pull them apart. At higher temperatures excess energy is available and atoms are more energised to fill coordinate saturated positions in a crystal lattice thus reducing the entropy of the crystal. The lattice energy of MgO if it were a single crystal of periclase is 3795 Kj mol-1 and is a major energy barrier to be overcome for hydration to occur.

Thermodynamic entropy (S) has the dimension of energy divided by temperature, and a unit of joules per kelvin (J/K) in the International System of Units. If the temperature K of calcination is higher then for the same amount of energy, entropy must decrease and the atoms within the crystal lattice are more ordered. The higher the temperature of calcination the greater the reduction in entropy of the crystal due to the ordering of atoms. Thermodynamically higher temperatures result in lower entropy and more ordered crystals. More ordered crystals have less unsaturated coordination sites and lower lattice energy. They are therefore less reactive. Conversely lower temperatures increase the entropy (J/K reduces) and the crystals are less ordered and more reactive.

TecEco describe reactivity in terms of the total lattice energy of magnesia as is a major kinetic barrier to be overcome and it of course influences solvation and activation energies. Crystalline magnesium oxide, or periclase, has a calculated lattice energy of 3795 Kj mol-1 which must be overcome for it to go into solution or for reaction to occur. Unfortunately neither lattice energy or the proportion of unsaturated coordination sites can be directly measured and are neither can easily be calculated which is probably why neither term is generally used to describe the reactivity of magnesia and specific surface area (SSA or Blaine) or sometime the result of a reactivity test such as with citric acid are used.

Thermodynamics of the Dissolution of Reactive MgO

Hess's law or the law of constant heat summation makes it clear that the amount of energy depends only on the states of the reactants and the state of the products, but not on the intermediate steps. When considering why magnesia hydrates and how quickly, both the enthalpy and entropy changes must be considered. First I will consider the enthalpy changes by breaking the process down into theoretical stages and analysing them in accordance with Hess's law.

Changes that Occur in the Dissolving Process.

MgO has a very high lattice energy suggesting strong ionic bonding forces. In spite of the strong attraction between positive ions (cations) and negative ions (anions) MgO will dissolve in water depending on the number of surface defects. Where ever there are surface defects the energy of the lattice is less because the coulomb forces acting between the particles are less. The coordination number of the surface or corner ions is decreased making them coordinately unsaturated and available for dissolution in water which is strongly polar. A sample of MgO which has very small crystallites with a lot of defects will statistically have a larger number of coordinately unsaturated atoms and thus be at a lower energy state than a corresponding sample with well formed crystallites of MgO. The lower the temperature of calcination the greater the number of defects, the lower the overall lattice energy and the more easily dissolution in water (hydration) occurs. Defects occur at low temperatures because there is insufficient energy to build well ordered lattices. At higher temperatures atoms can align themselves in saturated coordination and crystals grow more readily. See the discussion about entropy under the heading 'Thermodynamics of the Dissolution of Reactive MgO" above. See Doc Brown's Chemistry web site[10].

Water consists of highly polar molecules due to the huge electronegativity difference between hydrogen and oxygen (O > H hence the polarity of the bond δ-O-Hδ+). When salts dissolve in water a process of solvation occurs in which the ions become solvated by association with the solvent water molecules. In the case of water as the solvent, the process is called hydration and is exothermic because it involves particles coming together via intermolecular forces.

The magnesium ion is thought to produce both Mg++ ions and covalently bonded Mg(H2O)6]++ ions in solution and many other sometimes transitory species as well. Solvated ions are bigger than unsolvated ions which makes the distance between the positive and negative ion centres greater, and by the laws of electrostatics[11], the attractive forces are weakened. The hydration process, if a substance is "soluble" is therefore always exothermic.

The strong crystal lattice of MgO is broken down by the solvation process. As it dissolves the ions become free to move around in the water solvent.

The enthalpy of solution ΔHsolution (compound) is defined as the heat absorbed or released when 1 mole of the compound (the solute) dissolves in a solvent to form an 'infinitely' dilute solution where no further heat change takes place. The value depends on the structure and strength of the ionic lattice and the hydration enthalpies of the constituent ions.

The solvation process involves an increase in entropy - the solution is more disordered (more possible arrangements) than the pure liquid solvent and the more ordered lattice of MgO with very limited possible arrangements. Processes tend to go if there is an increase in entropy. See also the discussion about entropy under the heading 'Thermodynamics of the Dissolution of Reactive MgO" above.

Kinetic Factors Affecting the Dissolution of MgO

In spite of the importance of the process of dissolution of MgO, there is still some debate as to exact mechanisms. We suspect that this is because the predominance of the various mechanisms depends on pH and possibly also reactivity.

With high temperature calcination atoms have more energy and are more able to take up positions in crystals wherein surrounding coulomb forces are neutralised. i.e they have attractive and repulsive balance. Defects are minimised and coordinate saturation maximised. With low temperature calcination on the other hand crystallites with many defects are formed and there is insufficient energy to minimise coulomb forces. The result is a preponderance of surface atoms with unsaturated coordinates that are easily wrenched out as in the area of valleys, kinks, adatoms, terraces and steps in the diagram below of an MgO crystal surface having a cubic structure. The entropy is also increased - see also the discussion about entropy under the heading 'Thermodynamics of the Dissolution of Reactive MgO" above.

According to Fruwirth et. al. [9] "The dissolution and hydration kinetics of MgO single crystals and powder samples were investigated with regard to the H+ and Mg2+ concentrations and the temperature. The rate of dissolution of rotating MgO discs in buffered solutions was determined from measurements of [Mg2+] and those of the crystals and powder fractions were determined by pH and conductivity analysis. The degree of hydration was analysed by means of a thermogravimetric method. Several rate-controlling processes depending on pH were present at room temperature.

(1) At pH < 5 the rate-controlling step was proton attack followed by desorption of Mg2+ of OH- depending on the value of [Mg2+]. The rate was proportional to either -pH or pMg-pH. These processes are part of the overall neutralization reaction. MgO + 2H+→Mg2+ + H2O

(2) At pH ≈ 5 the rate-controlling step was a diffusion-limitation process due to protons. The rate was proportional to the proton concentration.

(3) At pH > 7 the rate-controlling step was OH- adsorption followed by Mg2+ and OH- desorption leading to a rate maximum. These processes are part of the overall dissolution reaction. MgO + H2O→Mg2+ + 2OH- The neutralization processes are interpreted in terms of irreversible thermodynamics yielding a linear dependence of the rate on pH or pMg-pH. It is concluded from conductivity and scanning electron microscopy measurements during and after hydration experiments that the hydration rate is controlled by the dissolution rate under given conditions. After a supersaturation period Mg(OH)2 precipitates preferentially at the MgO surface, so that an MgO lattice reaction can be excluded. All processes undergo an Arrhenius acceleration with increasing temperature (activation energy, 70 kJ mol-1) and the overall reactions are then limited by proton and OH- diffusion."

It is important to note that at high pH as in hydraulic cements these authors found "the hydration rate is controlled by the dissolution rate under given conditions" and from the above the dissolution rate is clearly proportional to the relative number of unsaturated co-ordination sites which determine overall lattice energy.

From the above theoretical analysis of the calcination, thermodynamics and kinetics it is clear that the hydration rate depends on the the dissolution rate which is a function of the temperature of calcination.The higher the temperatures of calcination, the slower the hydration rate.

Empirical Evidence of The Importance of Using Low Temperature Calcined Reactive Magnesia for Cements

One of the important features of TecEco cements is that we demonstrate for the first time that provided highly reactive magnesia that hydrates rapidly is used it can be blended in any proportion with other hydraulic binders.

TecEco prefer as low temperatures as technically possible for the production of reactive magnesia because if it does not hydrate rapidly enough there is a risk of dimensional distress as in the case of dead burned MgO produced as a result of impurities during the Portland cement clinker making process.

Our technology differs from that of the Chinese [13] in a number of ways including that we can add reactive magnesia in any proportion without dimensional issues whereas the Chinese must carefully regulate the small amount of higher temperature calcined magnesia they add to control shrinkage. See technical.rheological_shrinkage.php.

All minerals that hydrate or otherwise react in a setting concrete have associated molar volume changes as well as shape changes that result in an interlocked matrix of new minerals giving strength. As we state in our patents, the key to forming a sound concrete is to make sure that no mineral hydrates in a different rate order and that molar volume changes balance.

In relation to rate order consider a horse race. If a donkey were to be included it would complete its run well after the other horses reached the finish line thereby upsetting the celebrations of the winner. As we say in our patents “The key for the successful blending of magnesia and other cements and in particular Portland type cements is that the hydration rates of all components in the cement must be matched. In order to achieve this the magnesia component must be separately calcined at lower temperatures and in conditions that are suitable for the manufacture of reactive magnesia, ground to a fine size depending on the reactivity required and only then blended with other cementitious components, pozzolans or both.” In dense concretes in particular it is essential to make sure there is no risk of delayed hydration.

Whether or not there is expansion as magnesia hydrates also depends of overal system volume changes which are of two kinds: the molar volume changes as a result of reaction and volume change depending on whether the extent to which the system is closed. Whether or not the system is closed depends partly on whether the water required comes from mix water or outside the system during and after a concrete has set. If excessively from outside the system (binders + aggregates + water) expansion will ensue ( See technical.rheological_shrinkage.php). If this expansion is controlled as by the Chinese (See technical.chinese_mgo.php), it can usefully compensate for shrinkage, if not it can cause dimensional distress. Because reactive magnesia on the other hand hydrates much more rapidly and at a similar rate to Portland cement the water required comes from the mix and there is little or no dimensional influence because molar volumes roughly balance depending on the proportion of reactive magnesia.

With the use of reactive magnesia dimensional change is significantly reduced whatever the proportion mostly because of the kosmotrophic property of the Mg++ ion. Reactive magnesia reduces or prevents bleeding because of the high surface tension it introduces thereby closing the system and if there are no other losses or additions during setting, the amount of dimensional change is much less or even nil. See also technical.rheological_shrinkage.php

Generally the lower the temperature of calcination and finer the grind, the more reactive the magnesia and the faster it hydrates. In our patents we make it clear that “Suitable magnesia should be calcined at low temperatures (less than 750°C) and ground to greater than 95% passing 120 micron. Generally the lower the temperature of calcination and finer the grind, the more reactive the magnesia is and the faster it hydrates. Magnesia calcined as 650 °C passing 45 micron or less is better”. By using much more reactive magnesia hydration is in the same time frame and occurs in the same rate order as other components of a hydraulic cement and there is much less risk or dimensional distress. Just the right amount of mix water is consumed so that the expansion of the magnesia component just matches the net shrinkage of Portland cement minerals. As a result of this and restriction in fluid movement through capilliaries as a result of the strong charge in the magnesium ion, shrinkage is controlled in a safer way than by using carefully controlled amounts of less reactive magnesia as recently achieved by the Chinese wherein expansion of relatively unreactive magnesia matches the shrinkage of Portland cement based concretes. See technical.chinese_mgo.php

The magnesia used by the Chinese since 1972 is finely ground but generally calcined at at least 1000 degC (and usually more see Du [13] and Li [14]) and thus much less reactive than that used by TecEco. It has been used for controlled delayed expansive hydration in dam construction (See The Use of MgO by the Chinese) so that hydration with associated stoichiometric expansion "closely matches the shrinkage of
mass concrete as it cools" (See Du [13] ) In contrast TecEco use much more reactive magnesia so that it goes into solution more quickly and influences fresh concrete properties as well such as rheology, plastic and drying shrinkage. There are also many other beneficial side affects and the mechanism for controlling shrinkage is as explained quite different. (See The Use of MgO by the Chinese and Rheological and Shrinkage Reduction Affects of Adding Reactive Magnesia to Concretes.)

Du [13] shows on page 47 a table reproduced below that serves to indicate the enormous effect the calcination temperature of MgO has on the hydration rate expressed as the time taken for full hydration which is the important outcome of greater reactivity and this is commented on by numerous other authors including Birchal et. Al. in his conclusions on p1632[15]. Blaha et. Al in parts 2[16] and 3[17] also make it clear that from an experimental point of view the temperature of firing is all important explaining that the lower the temperature of calcination, the more reactive the magnesium oxide produced is and the faster the rate of hydration.

With corrections to the English shown the text of "Gelling Materials Science" [18] states as follows "Figure 3-3 (reproduced below) shows the inner surface area (specific surface area) for MgO made at different temperatures made using Mg(OH)2 as (a) raw material. At 4000C, the (specific surface area) distribution of MgO is (at a ) reached to maximum, S=
180m2/g. It will be decreased (decreases) when the temperature increases. At about 1000 deg C, the (specific) surface area is only ~10m2/g. This fact (is) also shown in Table
3-2 (also reproduced below.)"

Table 3-2 from "Gelling Materials Science"[18] reproduced above is not in conflict with Du's table shown earlier. It merely extends it to lower temperatures. Notice how steep the curve is - this means that our specification of 750 degrees C max with 650 degrees C preferred results in vastly different properties to those that result if calcination occurs at 850 - 1200 degrees C (Light burned according to Li [14]). The only problem with lower temperature calcination and we would prefer as low as technically possible is the technology. Low temperature calcination is very slowThe reader should also refer to The Use of MgO by the Chinese where the differences between the two technologies are addressed ).

The importance of calcination in relation to reactivity and thus hydration rate is also empirically confirmed independently by Blaha.[16] who examined in detail the affect of conditions of calcination on hydration rate. Blaha states in the abstract to the above paper "The specific surface area of the oxide decreases exponentially with increasing firing temperature." He produces the graph below at page 22.

Specific surface area of MgO vs temperature of firing. Time of firing is 60 minutes [17]

Because the relationship of specific surface area (as before a proxy measure of lattice energy) which in turn controls reactivity in relation to temperature is exponential as reported by Blaha, the difference in reactivity between calcining at a minimum of 800 degrees C compared to around 650 degrees C is almost double as can be seen in the above graph.

Blaha's work cited above is confirmed by Birchal et al.[15] This is further confirmed by Rocha et. al. more recently than our work when they say at page 819 "No effect from different particle sizes on the degree of magnesia hydration has been found (in relation to magnesia made at the same temperatures)."[19].

We conclude by making it clear that calcination temperature is very important and that without fluxes, no other citation or earlier literature than our patents suggests the use of reactive magnesia in hydraulic cements calcined anywhere near the low range specified. Furthermore the temperature of 750 degrees C is set by us as a maximum for calcination and as can be see from the tables and graphs of Du, Gelling Materials Science and Blaha, lower temperatures will produce more reactive product.

In our patents we make it clear that "The key for the successful blending of magnesia and other cements and in particular Portland type cements is that the hydration rates of all components in the cement must be matched." The emprical evidence is that calcination temperature is very important in relation to hydration rate and the properties of higher temperature calcined magnesia are very different.

The Realtive Importance of Grind Size

An important part of our teaching is that grind size makes nowhere near the difference to reactivity that temperature of firing does. It is however important to properly pack particles to improve rheology and many other properties [20].

Grind size is very important particularly in dense concretes where it is important to properly pack particles to reduce water demand and thus improve strength. The notion that the lower water demand of a concrete can be reduced by the addition of fine magnesia particles is foreign to many engineers but is technically possible. In relation to carbonating cements we teach the opposite. It is important to deliberately imperfectly pack particles to increase porosity beyond the percolation point. In relation to the percolation threshold see Garboczi [21] and Bentz [22]

We thus demonstrate that mangesia for TecEco cements does not necessarily require fine grinding as the size depends on the required packing, but the magnesia used must have low lattice energy. The ideal grinding size ranges depends on an analysis of the particle packing and the engineering objectives. In our Eco-Cements it is important to not pack particles perfectly so that gas permeability results whereas quite the opposite in our Tec-Cement concretes where it is important to pack particles as tightly as possible to minimise fineness water demand.

Smaller particles (unless they fit between other particles) generally have a high water demand in a concrete mix and as excess water weakens concrete an ideal reactive magnesia particle sizing is such that the grains fit in between other cement components. Another possible option yet to be tested is large so as not interfere with them. That is why the maximum particle size in our patents is around 120 micron.

The notion that the addition of fine particles of magnesia fitting between PC grains can actually reduce rather than increase water demand is foreign to many engineers but is technically the best solution for Tec-Cement concretes.

We explain above that Lattice energy is related to the state of disorder of magnesia. The higher the state of disorder, the more reactive the magnesia is. Disorder can be achieved to a much lesser extent by grinding. A more detailed discussion on the importance of particle packing is to be found under technical on the web site in our technical section The Importance of Particle Packing.

The lattice energy of periclase (the crystalline dead burned or hard burned form of magnesia) is high compared to most other minerals at 3795 Kj mol-1 and that is why it is used as a refractory. The fact that grind size makes nowhere near the difference to reactivity that temperature of firing does was probably first recognised by the Chinese, however this was in relation to Bajun Stone, a Sorel type composition. Blaha's work cited above is confirmed by Birchal et al.[15] This is further confirmed by Rocha et. al. more recently than our work when they say at page 819 "No effect from different particle sizes on the degree of magnesia hydration has been found (in relation to magnesia made at the same temperatures)"[19]

Lattice energy is related to the state of disorder of a crystal. The high the state of disorder, the more reactive a mineral such as magnesia is. Disorder can be achieved to a much lesser extent by grinding. To understand lattice energy and reactivity think about diamonds. Even if they could be ground, because diamond crystals have such a high lattice energy then it would not really matter how fine they were ground - they would still not be reactive.

[11] Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects. The attractive force is proportional to C+ x C- / d2, where d is the distance between the ion centres (atomic nuclei in simple 1 monatomic ions) and C+ and C- are the numerical charges on the cation and anion respectively and d is effectively the sum of the cation and anion radius for simple lattice structures.